EX-304 Network Analysis - Dec 2023 Question Paper

Under each question, How to answer lists the points an answer should cover, outlined by CampusPrep from the syllabus. Check the details against your textbook.

1. 7 Marks
   aUse mesh analysis to find current $i_o$ in the figure.

   

   How to answer

   • Define mesh currents and write KVL for each mesh
   • Incorporate dependent source 3i_o constraint relating mesh currents
   • Solve mesh equations for i_o
   • State final value of i_o with direction
2. 7 Marks
   bFor the network shown in below Figure below find $Z_{ab}$ and $I_o$.

   

   How to answer

   • Convert to phasor domain at omega=2: L to jwL, C to 1/jwC
   • Compute mutual impedance jwM with k=0.5
   • Find reflected impedance from secondary to primary
   • Compute Z_ab as parallel of capacitor branch and coupled-coil branch plus series terms and then I_o = V/Z_total
3. 7 Marks
   aDefine and explain the following with an example:

   1. i)Oriented Graph
   2. ii)Tree of a Graph
   3. iii)Tie set and a basic Tie set
   How to answer

   • Define oriented graph with directed branches and example
   • Define tree: connected, acyclic subgraph covering all nodes with example
   • Define tie-set and basic tie-set with respect to a tree with example
   • Give small graph sketches illustrating each
4. 7 Marks
   bIn the network shown in the figure, the switch is closed at $t = 0$ and there is no initial charge on either of the Capacitors. Find the current $i(t)$

   

   How to answer

   • Draw circuit for t>0 with initial conditions zero
   • Write integro-differential equation for i(t) or s-domain equation
   • Solve using Laplace / time-domain for series RLC with DC excitation
   • State i(t) expression showing damped nature
5. 7 Marks
   aState and explain Thevenin's theorem with an example.
   How to answer

   • State Thevenin statement: Vth in series with Zth
   • Explain steps to find Vth and Zth
   • Give simple example circuit with calculation
   • Mention source transformation / load connection
6. 7 Marks
   bCompute the current in 23 ohm resistor using super position theorem for the circuit shown.

   

   How to answer

   • Consider 200V alone (open current source) and find partial current
   • Consider 20A alone (short voltage source) and find partial current
   • Add algebraically for total current in 23 ohm
   • State final magnitude and direction
7. 7 Marks
   aShow that under the condition of maximum power transfer, the efficiency of the circuit is $50\%$.
   How to answer

   • Write power to load P = I^2 R_L with source R_s
   • Differentiate dP/dR_L = 0 to get R_L = R_s condition
   • Compute efficiency eta = P_out / P_in = 0.5
   • Conclude 50% efficiency at max power
8. 7 Marks
   bFor an RC series circuit, a sinusoidal voltage $V(t) = V_m \sin \omega t$ is applied at $t = 0$. Find the expression for transient current using Laplace transform approach.
   How to answer

   • Write time-domain KVL for RC with Vm sin wt
   • Take Laplace transform with zero initial condition
   • Solve for I(s) and take inverse Laplace
   • Separate transient vs steady-state terms
9. 7 Marks
   aState and explain Initial Value and Final value theorem.
   How to answer

   • State initial value theorem formula limit s->infinity
   • State final value theorem formula limit s->0
   • Explain conditions for existence (poles)
   • Give example application
10. 7 Marks
    bR-C series circuit is suddenly excited from a step voltage V. Derive an expression for the current as a function of time and draw the graph current Vs Time.
    How to answer

    • Write KVL V = Ri + (1/C) integral i
    • Solve first-order ODE with step input
    • Obtain i(t) = (V/R) e^{-t/RC}
    • Sketch exponentially decaying current vs time
11. 7 Marks
    aDetermine the Fourier series expansion (Trigonometrical form) for the wave form as shown in figure.

    

    How to answer

    • Identify period T and symmetry of triangular wave
    • Compute a0, an, bn integrals over period
    • Write trigonometric Fourier series sum
    • Mention odd/even harmonic content
12. 7 Marks
    bFind the transmission parameters of the following two port network.

    

    How to answer

    • Write port equations with 10 ohm, 20 ohm shunt and dependent source 3I1
    • Apply open/short conditions to find A,B,C,D
    • Solve for V1, I1 in terms of V2, -I2
    • Present ABCD matrix
13. 7 Marks
    aA two port network has the Z-parameters $Z_{11} = 20\Omega$, $Z_{22} = 30\Omega$ and $Z_{12} = Z_{21} = 40\Omega$ then find the ABCD and h-parameters for the network.
    How to answer

    • Recall Z to ABCD and Z to h conversion formulas
    • Substitute Z11=20, Z22=30, Z12=Z21=40
    • Compute determinant Delta_Z
    • Simplify to A,B,C,D and h11,h12,h21,h22
14. 7 Marks
    bFind the Z-parameters for the network shown in figure.

    

    How to answer

    • Apply open-circuit tests: I1=0, I2=0
    • Compute V1/I1, V2/I1 with output open etc.
    • Use voltage division in 1 ohm-2 ohm ladder
    • Assemble 2x2 Z matrix
15. 14 Marks
    Write a short notes on any two

    1. i)Incidence Matrix
    2. ii)Substitution Theorem
    3. iii)Short Circuit Admittance Parameters
    4. iv)Terminated Two Port Network
    How to answer

    • Choose any two topics from four
    • Give definition, formulas/matrix and brief explanation for each
    • Add small example or circuit illustration
    • Conclude with application